Found this interesting photo of a Curtiss Hawk 75 "Pratt & Whitney Special". Looks to me like a P-36/P-40 fuselage with a 2000hp Grumman F6F Hellcat style radial engine and nacelle.

Hey Jeff (Corsning),

Care to guesstimate a likely region of performance specifications? The original 870hp Hawk 75s could be up-engined to 1200-1650hp Allisons and Merlins with minimal structural changes (apart from the visually obvious lengthened rear fuselage), so confident that a 2000hp radial Pratt & Whitney could be made to fit without major structural redesign apart from the engine mounts. But what sort of performance improvements?

Obviously not worth the effort to divert engines from F4U and F6F production (or perhaps P-47 production) to continue with, but that could have been for many other reasons other than just performance.

Pratt & Whitney's H81A-Special NX28990?
This was an H81A airframe with the experimental P&W R-1830-SSC7-G engine with two-stage supercharger and by November
1942 it was, evidently, regularly waxing the Merlin powered P-40Fs stationed at a nearby base. Max speed on full military power
was 388mph at 24,000 ft.]

In 1940, Pratt & Whitney purchased from Curtiss a complete H81A-1 (P-40) airframe, without engine, with the intention of using it to test their R-1830-SSC7-G Twin Wasp. The resulting aircraft looked like a P-36 on steroids.

By November 10 1942 P&W reported that this hybrid plane performed much better than P-40F.

By December 29 1942, the Air Materiel Command ruled that "putting the R-1830 engine into the latest type P-40 aircraft is viewed as not worth the trouble and engineering time".

So 388 mph at 24,000 ft on 1200 hp. No bad. Certainly better altitude performance than the P-40s which generally had problems over 15-18,000 ft.

Tidbit more info from the Putnam volume on Curtiss aircraft: it was a Tomahawk II airframe c/n 17816 sold to P&W. (As also uncovered by Rick in his attached Curtiss document.) Additional photo of the aircraft in Putnam, similar to the front quarter photo attached above, but from higher angle. Unfortunately, no additional mention in the Putnam text.

Still like to do a Mythbusters on this and see what it could do with 2000 hp.

The -1 Merlin used in the P-40F had a single stage two speed supercharger, the -7 would be heavier as it had a two stage two speed one.

Not all P-40F were long tail as well, the earlier ones were not so would have been lighter.

It would have to be a big tail extension (and probably a bigger tail as well) to counterbalance the additional weight and power of a R-2800 even allowing for the lack of radiators. I suspect you would follow the sad route that Curtiss took and end up with an XP-60 ish plane ie basically a new plane.

As for the XP-60 - it had it's own cross to bear. It was originally designed to cater for a number of different engines, and subsequently redesigned and cobbled together with (in various configurations) contra-rotating props, single 4-blade props, extended radiator nacelle for in-line Packard, reconfigured for PW R-2800. It was never a clean design for a single task, and would have been encumbered with heritage structural arrangements from previous configurations. Take a single configuration, design a clean engine mount, and leave it alone, and you could probably clean up the drag reasonably. The final performance figures for the XP-60E could be improved upon, though perhaps not hugely.